Terminal 5 at London Heathrow

Tina and I went through Terminal 5 for the first time in August. We arrived in plenty of time (one of the downsides of living in Devon is the need to allow plenty of time for the connections to London airports). While we were waiting, having checked our hold baggage, we wandered from the terminal building back to the car-park and drop off points, which are in a separate multi-storey building. And there we discovered the personal rapid transport "pods" which carry people between the business car-park and the terminal. These pods could come out of a 1960s SF film; computer controlled vehicles, seating four people, running on a fixed track between the terminal and one of two stations in the car-park (not two car-parks, two stations in one car-park; the business users cannot be expected to walk too far, can they!) The journey took about 5 minutes.

It was the control rules which posed an interesting O.R. problem. At the terminal, there were four platforms where the pods could be boarded, and at the car-parks, there were two at each. So these constituted queues. Users arrive, and board a pod, if one is available. The pod departs, and -- if possible -- another one moves into place from a parking bay nearby. The control system moves empty pods around the tracks to wait in these three parking bays. So here are the questions:
(1) how many platforms should there be?
(2) what rules do you use to move empty pods around the tracks?
(3) how many pods do you need in the whole system?

We enjoyed the ride there and back again, and thought about the O.R. person who had thought through these questions.